Question

divide.\\((3x^2 + 16x + 19) \div (x + 3)\\)\
your answer should give the quotient and the remainder.\
quotient: \\(\square\\)\
remainder: \\(\square\\)

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(3x^2\) by the leading term of the divisor \(x\). So, \(\frac{3x^2}{x}=3x\). This is the first term of the quotient.

Step2: Multiply and subtract

Multiply the divisor \(x + 3\) by \(3x\), we get \(3x(x + 3)=3x^2+9x\). Now subtract this from the dividend: \((3x^2 + 16x + 19)-(3x^2+9x)=7x + 19\).

Step3: Divide the new leading term

Divide the leading term of the new dividend \(7x\) by the leading term of the divisor \(x\). So, \(\frac{7x}{x}=7\). This is the next term of the quotient.

Step4: Multiply and subtract again

Multiply the divisor \(x + 3\) by \(7\), we get \(7(x + 3)=7x+21\). Now subtract this from the new dividend: \((7x + 19)-(7x + 21)=-2\). This is the remainder.

Answer:

Quotient: \(3x + 7\)
Remainder: \(-2\)